The table below contains three samples obtained from three different populations

Question

The table below contains three samples obtained from three different populations. Please conduct an ANOVA test for the equality of the three population means and state if the test rejects the null hypothesis of the equality of the three means at the 80% confidence level?

Sample 1

A. The test fails to reject the null hypothesis of the equality of the three population means.

B. The test rejects the null hypothesis of the equality of the three population means.

C. The test is inconclusive

Sample 1

Sample 2 Sample 3 7 11 6 5 8 5 7 11 4 6 7 5 6 12 5 6 11 6 8 8 8 9 7 6 7 6 14 9 7 4 8 8 8 8 9 13 9 6 10 8 11 14 8 9 14 9 12 8 6 11 8 12

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

p - Value = 0.1149 which is less than 0.20 (For 80% confidence level, level of significance = 0.20), so we reject Ho.

The test rejects the null hypothesis of the equality of the three population means.

Option B is correct.

Column n Mean Std. Dev. Std. Error Sample 1 18 7.4444444 1.2472191 0.29397237 Sample 2 18 9.2222222 2.1572192 0.50846145 Sample 3 16 8.125 3.7215588 0.9303897

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